2.7 Life insurance premiums. Consider a group of 1, 000 college students in similar health conditions. By past statistics a student in the group will have 0.01% probability of death in each year. A life insurance company sets the premiums at $100 per year for each student for a coverage of $20, 000. Find (a) the probability that the company will lose money (b) the probability that the company will make at least $50, 000 each year (c) the minimum premiums for a coverage of $20, 000 to guarantee the company for mak- ing $50, 000 each year with at least 09 probability